Graph embedding techniques allow to learn high-quality feature vectors from graph structures and are useful in a variety of tasks, from node classification to clustering. Existing approaches have only focused on learning feature vectors for the nodes in a (knowledge) graph. To the best of our knowledge, none of them has tackled the problem of embedding of graph edges, that is, knowledge graph triples. The approaches that are closer to this task have focused on homogeneous graphs involving only one type of edge and obtain edge embeddings by applying some operation (e.g., average) on the embeddings of the endpoint nodes. The goal of this paper is to introduce Triple2Vec, a new technique to directly embed edges in (knowledge) graphs. Trple2Vec builds upon three main ingredients. The first is the notion of line graph. The line graph of a graph is another graph representing the adjacency between edges of the original graph. In particular, the nodes of the line graph are the edges of the original graph. We show that directly applying existing embedding techniques on the nodes of the line graph to learn edge embeddings is not enough in the context of knowledge graphs. Thus, we introduce the notion of triple line graph. The second is an edge weighting mechanism both for line graphs derived from knowledge graphs and homogeneous graphs. The third is a strategy based on graph walks on the weighted triple line graph that can preserve proximity between nodes. Embeddings are finally generated by adopting the SkipGram model, where sentences are replaced with graph walks. We evaluate our approach on different real world (knowledge) graphs and compared it with related work.

Machining processes are most accurately described using complex dynamical systems that include nonlinearities, time delays and stochastic effects. Due to the nature of these models as well as the practical challenges which include time-varying parameters, the transition from numerical/analytical modeling of machining to the analysis of real cutting signals remains challenging. Some studies have focused on studying the time series of cutting processes using machine learning algorithms with the goal of identifying and predicting undesirable vibrations during machining referred to as chatter. These tools typically decompose the signal using Wavelet Packet Transforms (WPT) or Ensemble Empirical Mode Decomposition (EEMD). However, these methods require a significant overhead in identifying the feature vectors before a classifier can be trained. In this study, we present an alternative approach based on featurizing the time series of the cutting process using its topological features. We utilize support vector machine classifier combined with feature vectors derived from persistence diagrams, a tool from persistent homology, to encode distinguishing characteristics based on embedding the time series as a point cloud using Takens embedding. We present the results for several choices of the topological feature vectors, and we compare our results to the WPT and EEMD methods using experimental time series from a turning cutting test. Our results show that in most cases combining the TDA-based features with a simple Support Vector Machine (SVM) yields accuracies that either exceed or are within the error bounds of their WPT and EEMD counterparts.

We introduce a new model for online ranking in which the click probability factors into an examination and attractiveness function and the attractiveness function is a linear function of a feature vector and an unknown parameter. Only relatively mild assumptions are made on the examination function. A novel algorithm for this setup is analysed, showing that the dependence on the number of items is replaced by a dependence on the dimension, allowing the new algorithm to handle a large number of items. When reduced to the orthogonal case, the regret of the algorithm improves on the state-of-the-art.

Learning Mahalanobis metric spaces is an important problem that has found numerous applications. Several algorithms have been designed for this problem, including Information Theoretic Metric Learning (ITML) by [Davis et al. 2007] and Large Margin Nearest Neighbor (LMNN) classification by [Weinberger and Saul 2009]. We consider a formulation of Mahalanobis metric learning as an optimization problem, where the objective is to minimize the number of violated similarity/dissimilarity constraints. We show that for any fixed ambient dimension, there exists a fully polynomial-time approximation scheme (FPTAS) with nearly-linear running time. This result is obtained using tools from the theory of linear programming in low dimensions. We also discuss improvements of the algorithm in practice, and present experimental results on synthetic and real-world data sets.

Continual learning is a critical ability of continually acquiring and transferring knowledge without catastrophically forgetting previously learned knowledge. However, enabling continual learning for AI remains a long-standing challenge. In this work, we propose a novel method, Prototype Reminding, that efficiently embeds and recalls previously learnt knowledge to tackle catastrophic forgetting issue. In particular, we consider continual learning in classification tasks. For each classification task, our method learns a metric space containing a set of prototypes where embedding of the samples from the same class cluster around prototypes and class-representative prototypes are separated apart. To alleviate catastrophic forgetting, our method preserves the embedding function from the samples to the previous metric space, through our proposed prototype reminding from previous tasks. Specifically, the reminding process is implemented by replaying a small number of samples from previous tasks and correspondingly matching their embedding to their nearest class-representative prototypes. Compared with recent continual learning methods, our contributions are fourfold: first, our method achieves the best memory retention capability while adapting quickly to new tasks. Second, our method uses metric learning for classification, and does not require adding in new neurons given new object classes. Third, our method is more memory efficient since only class-representative prototypes need to be recalled. Fourth, our method suggests a promising solution for few-shot continual learning. Without tampering with the performance on initial tasks, our method learns novel concepts given a few training examples of each class in new tasks.

We establish the first nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators where feature vectors reside in metric spaces. Our bounds imply rates of strong consistency for these nonparametric estimators and, up to a log factor, match an existing lower bound for conditional CDF estimation. Our proof strategy also yields nonasymptotic guarantees for nearest neighbor and kernel variants of the Nelson-Aalen cumulative hazards estimator. We experimentally compare these methods on four datasets. We find that for the kernel survival estimator, a good choice of kernel is one learned using random survival forests.

We study online reinforcement learning for finite-horizon deterministic control systems with {\it arbitrary} state and action spaces. Suppose that the transition dynamics and reward function is unknown, but the state and action space is endowed with a metric that characterizes the proximity between different states and actions. We provide a surprisingly simple upper-confidence reinforcement learning algorithm that uses a function approximation oracle to estimate optimistic Q functions from experiences. We show that the regret of the algorithm after $K$ episodes is $O(HL(KH)^{\frac{d-1}{d}}) $ where $L$ is a smoothness parameter, and $d$ is the doubling dimension of the state-action space with respect to the given metric. We also establish a near-matching regret lower bound. The proposed method can be adapted to work for more structured transition systems, including the finite-state case and the case where value functions are linear combinations of features, where the method also achieve the optimal regret.

Model-free Reinforcement Learning (RL) algorithms such as Q-learning [Watkins, Dayan 92] have been widely used in practice and can achieve human level performance in applications such as video games [Mnih et al. 15]. Recently, equipped with the idea of optimism in the face of uncertainty, Q-learning algorithms [Jin, Allen-Zhu, Bubeck, Jordan 18] can be proven to be sample efficient for discrete tabular Markov Decision Processes (MDPs) which have finite number of states and actions. In this work, we present an efficient model-free Q-learning based algorithm in MDPs with a natural metric on the state-action space--hence extending efficient model-free Q-learning algorithms to continuous state-action space. Compared to previous model-based RL algorithms for metric spaces [Kakade, Kearns, Langford 03], our algorithm does not require access to a black-box planning oracle.

In this paper we address the problem of discovering a small set of frequent serial episodes from sequential data so as to adequately characterize or summarize the data. We discuss an algorithm based on the Minimum Description Length (MDL) principle and the algorithm is a slight modification of an earlier method, called CSC-2. We present a novel generative model for sequence data containing prominent pairs of serial episodes and, using this, provide some statistical justification for the algorithm. We believe this is the first instance of such a statistical justification for an MDL based algorithm for summarizing event sequence data. We then present a novel application of this data mining algorithm in text classification. By considering text documents as temporal sequences of words, the data mining algorithm can find a set of characteristic episodes for all the training data as a whole. The words that are part of these characteristic episodes could then be considered the only relevant words for the dictionary thus resulting in a considerably reduced feature vector dimension. We show, through simulation experiments using benchmark data sets, that the discovered frequent episodes can be used to achieve more than four-fold reduction in dictionary size without losing any classification accuracy.

Elizabeth Keatinge tells us about Elon Musk's DNA Friend makes fun of the at-home DNA testing craze. The government's contempt of court case against Tesla CEO Elon Musk is moving forward. Federal Judge Alison Nathan has set a court date of April 4 to hold oral arguments. The Securities and Exchange Commission is asking Nathan to find Musk in contempt for allegedly violating terms of an October court-approved securities fraud settlement with a Feb. 19 tweet. In the tweet, Musk wrote: "Tesla made 0 cars in 2011, but will make around 500k in 2019."